Two nonlinear dispersive wave equations arising in elasto-plastic flow have been investigated for self-adjointness. For these equations their symmetries are calculated and conservation laws are constructed using two different methods: an old method based on Noether´s Theorem and a new one developed by Prof. Nail Ibragimov. The new method works for a larger number of equations than the old one. It is complementing the old one in the way that it gives some conservation laws that otherwise would have been impossible to obtain.